Barry Robson was the villain of the piece, seeing his spot-kick blocked by Karim Zaza after Shaun Maloney had been brought down by Steve Olfers in the area.
The game also ended in farce as the Danes were reduced to ten men with 11 minutes left to play when Michael Beauchamp was sent off for a professional foul, despite Michael Jakobsen being the culprit.
It was the visitors that had come closest to making the breakthrough before Robson's miss, with Jeppe Curth finding space behind the home defence before shooting wide as Artur Boruc closed in.
The rest of the first half was mainly forgettable, with chances few and far between for both sides.
After the break Shunsuke Nakamura's pass almost gave Georgios Samaras the chance to open the scoring, but the Greek striker couldn't direct his effort on target from an acute angle.
Samaras then passed up another opening with 15 minutes left to play deciding to cut back inside at the far post and being crowded out after being fed in by Jan Vennegor of Hesselink.
After Beauchamp's dismissal, Zaza ensured his side earned a draw by superbly tipping away the resulting free-kick from Nakamura and Aalborg withstood further late pressure to secure a hard-earned point.